Final answer:
Sherlock Holmes deduces that the person who has visited them is not the actual Dr. Mortimer based on a discrepancy in the visitor's attire, specifically in the way the boots are worn.
Step-by-step explanation:
In "The Hound of the Baskervilles," Sherlock Holmes deduces that the person who has visited them is not the actual Dr. Mortimer through a discrepancy in the visitor's attire. He notices that the visitor's boots are not worn in the same way as a medical professional would wear them. This small detail raises suspicion and leads Holmes to question the visitor's identity.